No problem. It's only a 5% difference in v
It is not hard. 220VAC is standard and common for house hold and residential applications in India.
The transformer will act as a step down transformer in the ratio of 240 to 208. This will reduce the 208 input to 180.
Short answer: No. (unless you like ruining motors) Longer answer: Not really, but there are some motors that can be re-wired so that instead of 440v they will run on 220v. However, this is not that common. Conclusion: Check the motor to see if it is dual-voltage on it's nameplate. If it is, you can re-connect it to work on 220v. If it is NOT a dual-voltage motor, you will absolutely ruin it if you connect it to 220v.
220VAC 50Hz
This is a 15% overvoltage to the motor, which is generally outside the specifications for a motor spec'd at 208v (typically up to 10% overvoltage is tolerable). Your 240 volt source may be as much as 105% of 240 / 252 volts at times. A buck/boost transformer should be used, unless the motor is designed to be used at 240 volts.
220VAC at 50Hz
120/208VAC
Your question is confusing. First off a battery charger puts out DC voltage not AC. If you are asking if you can run a 120 volt battery charger on a 220 volt circuit the answer is no you cannot. That would destroy the charger.
motor energy
You can but the motor may not run, however you will not burn the motor.
To do a motor solo run test you need to connect the motor to a power supply. Next, you observe the motor's vibration, temperature, and sounds.